Not at all, no. It's such an arbitrary thing and people in football usually have an attitude where the teams that were big or good in their childhood are the only ones that mattered, ever have mattered and ever should matter.
I love football, I love talking about different teams and who is good in the here and now without getting into bitter arguments about who 'earned' their success or 'bought' their success, that sort of stuff. If fans of teams that are supposedly 'bigger than City' are bitter that City is now beating their team, they should hang their heads in shame for having a decades long headstart and still losing.
If you ask many a Madrid fan often times they'll say Barcelona isn't actually a big club at all and only become relevant with Cruyff and yet in my teenage years Real Madrid didn't get out of a CL round of sixteen for about seven years straight despite outspending everybody else.
When Man Utd had the most money and won the most things they were seen as a plastic new kid on the block, but now they are supposedly the soulful traditional team taking on the evil antagonist in City. It's all a load of nonsense.